Grillen Nørrebro looks like an American upscale burger joint. It has the same vibe, feel. And we can't be 100% sure, but it seemed like guy in charge of the kitchen was American, which obviously helps.
This place is busy, so don't expect a super quick meal. It's not horribly priced, either. The burgers are quite tasty, with several different options of toppings. Whatever has onion rings on it is quite popular, if the passing serving trays were any indication. Like all places in Denmark, you don't get to dictated the "well-done-ness" of your food. Which is a better way that trying to control everything. The chefs have a plan. Let them execute on it.
All burgers come with thick, steak fries with a variety of seasoning and dipping sauces. WARNING: Getting the chili dusted fries AND the super hot sauce is a bad, bad idea. Because WOW!
They also sell Ben & Jerry's milkshakes. It was OK, but probably not worth the $9 USD.